4y-1/3y=5

Solution for 4y-1/3y=5 equation:

4y-1/3y=5

We move all terms to the left:

4y-1/3y-(5)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We multiply all the terms by the denominator


4y*3y-5*3y-1=0

Wy multiply elements

12y^2-15y-1=0

a = 12; b = -15; c = -1;
Δ = b2-4ac
Δ = -152-4·12·(-1)
Δ = 273
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{273}}{2*12}=\frac{15-\sqrt{273}}{24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{273}}{2*12}=\frac{15+\sqrt{273}}{24}
$